Adjoint-based full-order and reduced-order approaches for gust mitigation

Two different adjoint-based approaches are developed here for gust mitigation of twodimensional or three-dimensional wing models in oscillatory heaving-pitching motion. One approach is based on a full-order model (FOM), i.e., Navier-Stokes equations, where noncylindrical calculus is implemented for moving boundary effect, and the other is based on a global reduced-order model (ROM), which models fluid flow and moving solid boundary in a global framework. When the lift performance was affected by either streamwise or transverse gusts, an objective function was designed to reduce the oscillation and keep the same lift to maintain a stable flight in gust. The goal was achieved by the optimal control of wing motions using the adjoint-FOM approach or the adjoint-ROM approach. In the study, the streamwise gust was successfully mitigated by reducing the amplitude of the heaving-pitching motion, and the transverse gust was mitigated by reducing the oscillation amplitude and decreasing the mean angle of attack at the same time. The adjoint-FOM approach provides better accuracy and can handle stronger gusts at the cost of longer computational time. The adjoint-ROM approach has lower accuracy and can only handle two-dimensional cases with weaker gusts, but it has its own advantage of requiring much less computational time and makes real-time control possible.